Odd rendering issue -- Extra lines
Welp, I didn't determine the exact issue for all situations, but it seemed some meshes had doubles issues, faces issues, normals issues, etc.  You could do things like select a vertex around a bad area and hit Ctrl+ to select similar ones, but the bad one wouldn't get selected.

To fix, I ended up selecting whole areas that were at issue and deleting them.  I then either rebuilt them or duplicated other similar areas and placing them there.

I hate not knowing the exact issue, but at least I'm up and running.  

Thanks to those who took the time!